Answered: The central tail feathers of the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Question

The central tail feathers of the long-tailed finch (Poephila acuticauda) are a sexually dimorphic trait hypothesized to play a role in sexual selection. The longer tail feathers in males cost energy to produce, and this is thought to signal the male’s excellent health condition. The table contains the lengths of the central tail feathers (average of the two central feathers, in millimeters) of 20 male and 21 female long-tailed finches.

(a) Compute a 95% confidence interval for the difference in mean response μf − μm based on df = 32.

(b) Test whether the means are equal or not.

Statistic X
Female
Male
65.31
82
S
7.7
11.6
n
21
20

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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